The shield that never was: societies with single-peaked preferences are more open to manipulation and control

@article{Faliszewski2009TheST,
  title={The shield that never was: societies with single-peaked preferences are more open to manipulation and control},
  author={Piotr Faliszewski and Edith Hemaspaandra and Lane A. Hemaspaandra and J{\"o}rg Rothe},
  journal={ArXiv},
  year={2009},
  volume={abs/0909.3257}
}
Much work has been devoted, during the past twenty years, to using complexity to protect elections from manipulation and control. Many results have been obtained showing NP-hardness shields, and recently there has been much focus on whether such worst-case hardness protections can be bypassed by frequently correct heuristics or by approximations. This paper takes a very different approach: We argue that when electorates follow the canonical political science model of societal preferences the… 

Figures and Tables from this paper

Reinstating Combinatorial Protections for Manipulation and Bribery in Single-Peaked and Nearly Single-Peaked Electorates
TLDR
In single- peaked and nearly single-peaked electorates, if voters are allowed to submit top-truncated ballots, then the complexity of manipulation and bribery for many voting rules increases from being in P to being NP-complete.
The Complexity of Nearly Single-Peaked Consistency 1
TLDR
It is proved that determining whether a given profile is nearly single-peaked is in many cases NPcomplete, and the relations between several notions of nearly singlepeakedness are explored.
Challenges to complexity shields that are supposed to protect elections against manipulation and control: a survey
TLDR
This work surveys and discusses some recent results on challenges to complexity results for manipulation and control, including typical-case analyses and experiments, fixed-parameter tractability, domain restrictions, and approximability.
Modeling Single-Peakedness for Votes with Ties
TLDR
This work studies the computational complexity of manipulation for votes with ties for the standard model of single-peaked preferences and for single-plateaued preferences and shows that these models avoid the anomalous complexity behavior exhibited by the other models.
Where are the hard manipulation problems?
  • T. Walsh
  • Computer Science, Economics
    J. Artif. Intell. Res.
  • 2011
TLDR
Empirical studies are shown to be useful in improving the understanding of computational complexity in voting and manipulation, and two settings are considered which represent the two types of complexity results: manipulation with unweighted votes by a single agent, and manipulation with weighted Votes by a coalition of agents.
On the likelihood of single-peaked preferences
TLDR
A very general upper bound result is provided for domain restrictions that can be defined by certain forbidden configurations that implies that many domain restrictions (including the single-peaked restriction) are very unlikely to appear in a random election chosen according to the Impartial Culture assumption.
Weighted electoral control
TLDR
This paper studies the complexity of controlling the outcome of weighted elections through adding and deleting voters, and obtains polynomial-time algorithms, NP-completeness results, and for many NP-complete cases, approximation algorithms.
Is computational complexity a barrier to manipulation?
  • T. Walsh
  • Computer Science
    Annals of Mathematics and Artificial Intelligence
  • 2011
TLDR
This survey article summarizes the evidence for and against computational complexity being a barrier to manipulation, and looks both at techniques identified to increase complexity, as well as other features that may change the computational complexity of computing a manipulation.
Preferences Single-Peaked on a Circle
TLDR
This work proves that Proportional Approval Voting can be computed in polynomial time for profiles that are single-peaked on a circle, and gives a fast recognition algorithm of this domain, provides a characterisation by finitely many forbidden subprofiles, and shows that many popular single- and multi-winner voting rules are polynometric-time computable on this domain.
...
...

References

SHOWING 1-10 OF 54 REFERENCES
Junta distributions and the average-case complexity of manipulating elections
TLDR
It is demonstrated that NP-hard manipulations may be tractable in the average-case, and a family of important voting protocols is susceptible to manipulation by coalitions, when the number of candidates is constant.
Llull and Copeland Voting Broadly Resist Bribery and Control
TLDR
This paper proves that an election system developed by the 13th century mystic Ramon Llull and the well-studied Copeland election system are both resistant to all the standard types of (constructive) electoral control other than one variant of addition of candidates.
Single transferable vote resists strategic voting
TLDR
Evidence that Single Tranferable Vote (STV) is computationally resistant to manipulation is given and it is proved that it is NP-complete to recognize when an STV election violates monotonicity, suggesting that non-monotonicity in STV elections might be perceived as less threatening since it is in effect “hidden” and hard to exploit for strategic advantage.
Voting cycles and the structure of individual preferences
Empirical studies have shown that cyclical preferences are infrequent, but they have been less clear about why. Using ‘thermometer’ ratings from nationally-representative samples of the U.S., we
Hybrid Elections Broaden Complexity‐Theoretic Resistance to Control
Electoral control refers to attempts by an election's organizer (“the chair”) to influence the outcome by adding/deleting/partitioning voters or candidates. The important paper of Bartholdi, Tovey,
When are elections with few candidates hard to manipulate?
TLDR
This article characterize the exact number of candidates for which manipulation becomes hard for the plurality, Borda, STV, Copeland, maximin, veto, plurality with runoff, regular cup, and randomized cup protocols and shows that for simpler manipulation problems, manipulation cannot be hard with few candidates.
Nonexistence of Voting Rules That Are Usually Hard to Manipulate
TLDR
It is shown that it is in fact impossible to design a rule under which finding a beneficial manipulation is usually hard, if the rule is also required to satisfy another property: a large fraction of the manipulable instances are both weakly monotone, and allow the manipulators to make either of exactly two candidates win.
A sufficient condition for voting rules to be frequently manipulable
TLDR
A sufficient condition for a voting rule to be randomly manipulable with a probability of Ω(1/n) for at least one voter, when the number of alternatives is held fixed is given.
...
...